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In this paper we provide a thorough investigation of the cluster sampling scheme for Morris' elementary effects method (MM), a popular model‐free factor screening method originated in the setting of design and analysis of computational experiments. We first study the sampling mechanism underpinning the two sampling schemes of MM (i.e., cluster sampling and noncluster sampling) and unveil its nature as a two‐level nested sampling process. This in‐depth understanding sets up a foundation for tackling two important aspects of cluster sampling: budget allocation and sampling plan. On the one hand, we study the budget allocation problem for cluster sampling under the analysis of variance framework and derive optimal budget allocations for efficient estimation of the importance measures. On the other hand, we devise an efficient cluster sampling algorithm with two variants to achieve enhanced statistical properties. The numerical evaluations demonstrate the superiority of the proposed cluster sampling algorithm and the budget allocations derived (when used both separately and in conjunction) to existing cluster and noncluster sampling schemes.

 

This paper proposes two fully sequential procedures for selecting the best system with a guaranteed probability of correct selection (PCS). The main features of the proposed procedures include the following: (1) adopting a Bonferroni-free model that overcomes the conservativeness of the Bonferroni correction and delivers the exact probabilistic guarantee without overshooting; (2) conducting always valid and fully sequential hypothesis tests that enable continuous monitoring of each candidate system and control the type I error rate (or equivalently, PCS) at a prescribed level; and (3) assuming an indifference-zone-flexible formulation, which means that the indifference-zone parameter is not indispensable but could be helpful if provided. We establish statistical validity and asymptotic efficiency for the proposed procedures under normality settings with and without the knowledge of true variances. Numerical studies conducted under various configurations corroborate the theoretical findings and demonstrate the superiority of the proposed procedures. Funding: W. Wang and H. Wan were supported in part by CollinStar Capital Pty Ltd. X. Chen was supported in part by the National Science Foundation [Grant IIS-1849300 and CAREER CMMI-1846663]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2447 .